[1]赵君平,管平.考虑热效应时半导体方程整体弱解的存在性[J].东南大学学报(自然科学版),2003,33(2):226-231.[doi:10.3969/j.issn.1001-0505.2003.02.028]
 Zhao Junping,Guan Ping.Existence of global weak solutions to the semiconductor equations with heat effect[J].Journal of Southeast University (Natural Science Edition),2003,33(2):226-231.[doi:10.3969/j.issn.1001-0505.2003.02.028]
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考虑热效应时半导体方程整体弱解的存在性()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
33
期数:
2003年第2期
页码:
226-231
栏目:
数学、物理学、力学
出版日期:
2003-03-20

文章信息/Info

Title:
Existence of global weak solutions to the semiconductor equations with heat effect
作者:
赵君平 管平
东南大学数学系,南京 210096
Author(s):
Zhao Junping Guan Ping
Department of Mathematics, Southeast University, Nanjing 210096, China
关键词:
整体弱解 存在性 先验估计 紧性引理 热效应
Keywords:
global weak solution existence a priori estimates compactness principle heat effect
分类号:
O175.29
DOI:
10.3969/j.issn.1001-0505.2003.02.028
摘要:
研究半导体物理中出现的漂移-扩散模型,在考虑热效应时,这是一个关于带电粒子浓度n,p,静电位ψ和温度θ的抛物-椭圆耦合方程组,并带有混合初边值条件.对温度效应项H=·(a(ψ)Jn+b(ψ)Jp)时讨论了初值分别在L+(Ω)L2+(Ω)2时该方程组的可解性.利用正则化方法和适当的函数变换,使抛物型方程的解具有正下界n,p≥δ>0,同时得出一系列先验估计.然后利用紧性引理和Schauder不动点定理,得出原问题整体弱解的存在性.
Abstract:
The drift-diffusion model with heat effect arising in semiconductor physics, which is a parabolic-elliptic coupled system mathematically with unknown functions such as densities of carriers, n,p, electrostatic potential ψ and temperature θ and subjected to mixed boundary conditions, is considered. Under the hypothesis that the temperature effect term is of the form H=·(a(ψ)Jn+b(ψ)Jp), we investigate the solvability of the system for the initial values in L+(Ω) and L2+(Ω)2, respectively. At first, we prove that the solutions have a positive lower bound n,p≥δ>0 by using regularized method and appropriate variable transformation. Then we conclude the global existence of the problem in terms of a priori estimates, compactness principle and Shauder fixed point theorem.

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备注/Memo

备注/Memo:
作者简介: 赵君平(1972—),女,硕士, jpzhao87@sohu.com; 管平(联系人),男,教授,pguan@seu.edu.cn.
更新日期/Last Update: 2003-03-20